Symptom. Goths had been around since the late 1970s and their surge in popularity during the late 80s/ early 90s both predated and anticipated The Crow. Goth was simply part of the American zeitgeist.
The Crow certainly helped give the subculture a boost, and may have been at least partially responsible for the subsequent explosion of late 90s Mansonite/ Babygoths, but the film was simply riding the wave, in much the same way as The Matrix surfed the rising tide of Cyberpunk.